## Exercise 1 ##

c2f <- function(T, inverse=FALSE){
  
  if (inverse){
    tmp <- (T - 32) * (5/9)
  } else {
    tmp <- (T * (9/5)) + 32
  }
  return(tmp)
}

c2f(212, inverse=TRUE)

## Exercise 2 ##

myfib <- function(n){
  st <- c(1,1)
  mysum <- st[2]
  if (n>=3){
    for (i in 3:round(n,0)){
      mysum <- st[1] + st[2]
      st <- c(st[2],mysum)
    }
  } else {
    if (n<=0){
      stop("Cannot compute Fibonacci series for a negative number")
    } 
  }
  return(st[2])
}

## Exercise 3 ##

ckprime <- function(n){
  n <- abs(round(n,0))
  flag <- FALSE
  i <- 2
  while(i < n & !flag){

    if (n%%i==0){
      print(i)
      flag <- TRUE
    }
    i <- i + 1
  }
  if (flag){
    tmp <- paste(n, "is not a prime number.")
  } else {
    tmp <- paste(n, "is a prime number.")
  }
  return(flag)
}

# Optimize, do not check for even numbers
ckprime2 <- function(n){
  n <- abs(round(n,0))
  flag <- FALSE
  if (n%%2==0 & n!=2){
    flag <- TRUE
  } else {
    i <- 3
    while(i < n & !flag){
      if (n%%i==0)
        flag <- TRUE
      i <- i + 2
    }
  }
  if (flag){
    tmp <- paste(n, "is not a prime number.")
  } else {
    tmp <- paste(n, "is a prime number.")
  }
  return(flag)
}

system.time(ckprime(7919))
system.time(ckprime2(7919))



## Ex 4 ##
get.divisors <- function(n){

  # Is the input 0?
  if (n == 0){
    mydiv <- 0 # Divisors should be 0
  } else {
    mydiv <- 1 # Initialize the divisors vector
    for (i in 2:(n-1)){
      tmp <- ckprime2(i) # Check if the divisor is a prime number
      if (!tmp){
        if (all.equal(n%%i, 0) == TRUE) 
          mydiv <- c(mydiv,i) # Add only divisors
      }
    }
  }
  return(mydiv)
}

ckperfect <- function(n){
  if (n%%1!=0){
    stop("Given a float number, integer is needed!")
  } else {
    N <- n
    if (n<0) # Check for the sign
      N <- abs(n)

    # Get the divisors
    mydiv <- get.divisors(N) 
    
    # Check equality on the sum
    if (abs(sum(mydiv) - N)<=1e-10){
      tmp <- TRUE
    } else {
      tmp <- FALSE
    }
    # Return TRUE if it is a perfect number, otherwise return FALSE
    return(tmp)
  }
}

ckperfect(6)
ckperfect(8)
ckperfect(0.3)

## Excercise 6

par(mfrow=c(2,1))
## Varying the mean
aa <- sapply(seq(-3,3,length=8),function(x){
  x <- rnorm(1000,mean=x,sd=1)
  return(x)
})


  bb <- matrix(0,ncol=8,nrow=1000)
for (i in seq(-3,3,length=8)){
  bb[,i] <- rnorm(1000,mean=i,sd=1)
}


aa <- sapply(seq(-3,3,length=8),rnorm, mean=x)







mycol <- terrain.colors(8)
for (i in 1:ncol(aa)){
  if (i == 1){
    plot(density(aa[,i]),xlim=c(min(aa),max(aa)), col=mycol[i], main="Mean in [-3,3]")
    abline(v=mean(aa[,i]),lty=2, col=mycol[i])
  } else {
    lines(density(aa[,i]),xlim=c(min(aa),max(aa)), col=mycol[i])
    abline(v=mean(aa[,i]),lty=2, col=mycol[i])
  }
}

## Varying the variance
aa <- lapply(seq(0.1,2,length=8),function(x){
  x <- density(rnorm(1000,m=0,sd=x))
  return(x)
})
lim <- sapply(aa,function(x){c(min(x$x), max(x$x),min(x$y), max(x$y))})
lim <- c(min(lim[1,]), max(lim[2,]),min(lim[3,]), max(lim[4,]))

for (i in 1:length(aa)){
  if (i == 1){
    plot(aa[[i]]$x,aa[[i]]$y, col=mycol[i],main="Sd in [0.1,2]",type="l", xlim=lim[1:2], ylim=lim[3:4], xlab="x", ylab="Density")
  } else {
    lines(aa[[i]]$x, aa[[i]]$y, col=mycol[i])
  }
}

# Solution 2
ma <- lapply(seq(-3,3,length=8),function(x){
  x <- rnorm(1000,m=x,sd=1)
  return(x)
})
sa <- lapply(seq(0.1,2,length=8),function(x){
  x <- rnorm(1000,m=0,sd=x)
  return(x)
})


df <- data.frame(X=c(unlist(ma),unlist(sa)), Y=c(unlist(ma),unlist(sa)) ,
                 SD=c(rep(1,1000*8), rep(seq(0.1,2,length=8), each=1000)),
                 M=c( rep(seq(-3,3,length=8), each=1000), rep(0,1000*8)),
                 PLFLAG=c(rep("Mean",1000*8), rep("Sd", 1000*8)))

library(lattice)
densityplot(~X|PLFLAG, groups=SD+M, data=df,plot.points=FALSE, layout=c(1,2),
            scales=list(relation="free"), as.table=TRUE)



## Exercise 7
mycol <- rev(heat.colors(30)[seq(1,20,2)])
for (i in seq(1,5,length=10)){
  n <- 10^i
  tmp <- rnorm(n)
  if (i == 1){
    plot(density(tmp), ylim=c(0,0.6), col=mycol[i])
  } else {
    lines(density(tmp), col=mycol[i])
  }
}


## Exercise 8
data(Pima.tr, package="MASS")
table(Pima.tr$type)
library(lattice)
library(latticeExtra)
hh <- histogram(~age+bmi+glu|type, data=Pima.tr, scales=list(relation="free"))
useOuterStrips(hh)